We study how Berry phase affects the Wigner crystal (WC) state of a two-dimensional electron system. We consider first a model of Bernal bilayer graphene with a perpendicular displacement field, and we show that Berry curvature leads to a new kind of WC state in which the electrons acquire a spontaneous orbital angular momentum when the displacement field exceeds a critical value. We determine the phase boundary of the WC state in terms of electron density and displacement field at low temperature. We then derive the effective Hamiltonian governing the ordering of the physical electron spin. We show that this Hamiltonian contains a chiral term capable of driving the system into chiral spin-density wave or spin liquid phases. The phenomena we discuss are relevant for the valley-polarized Wigner crystal phases observed in multilayer graphene.

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• Berry curvature
• Bilayer graphene
• Graphene
• Quantum spin models
• Wigner crystal